Sampling rate effects on measurements of correlated and biased random walks

When observing the two-dimensional movement of animals or microorganisms, it is usually necessary to impose a fixed sampling rate, so that observations are made at certain fixed intervals of time and the trajectory is split into a set of discrete steps. A sampling rate that is too small will result in information about the original path and correlation being lost. If random walk models are to be used to predict movement patterns or to estimate parameters to be used in continuum models, then it is essential to be able to quantify and understand the effect of the sampling rate imposed by the observer on real trajectories. We use a velocity jump process with a realistic reorientation model to simulate correlated and biased random walks and investigate the effect of sampling rate on the observed angular deviation, apparent speed and mean turning angle. We discuss a method of estimating the values of the reorientation parameters used in the original random walk from the rediscretized data that assumes a linear relation between sampling time step and the parameter values.     

Foray search: an effective systematic dispersal strategy in fragmented landscapes

In the absence of evidence to the contrary, population models generally assume that the dispersal trajectories of animals are random, but systematic dispersal could be more efficient at detecting new habitat and may therefore constitute a more realistic assumption. Here, we investigate, by means of simulations, the properties of a potentially widespread systematic dispersal strategy termed "foray search." Foray search was more efficient in detecting suitable habitat than was random dispersal in most landscapes and was less subject to energetic constraints. However, it also resulted in considerably shorter net dispersed distances and higher mortality per net dispersed distance than did random dispersal, and it would therefore be likely to lead to lower dispersal rates toward the margins of population networks. Consequently, the use of foray search by dispersers could crucially affect the extinction-colonization balance of metapopulations and the evolution of dispersal rates. We conclude that population models need to take the dispersal trajectories of individuals into account in order to make reliable predictions.     

The evolution of dispersal in random environment

In this paper we introduce a stochastic model for a population living and migrating between s sites without distinction in the states between residents and immigrants. The evolutionary stable strategies (ESS) is characterized by the maximization of a stochastic growth rate. We obtain that the expectation of reproductive values, normalized by some random quantity, are constant on all sites and that the expectation of the normalized vector population structure is proportional to eigenvector of the dispersion matrix associated to eigenvalue one, which are, in some way, analogous to the results obtained in the deterministic case.     

Why the null matters: statistical tests,random walks and evolution

A number of statistical tests have been developed to determine what type of dynamics underlie observed changes in morphology in evolutionary time series, based on the pattern of change within the time series. The theory of the scaled maximum, the log-rate-interval (LRI) method, and the Hurst exponent all operate on the same principle of comparing the maximum change, or rate of change, in the observed dataset to the maximum change expected of a random walk. Less change in a dataset than expected of a random walk has been interpreted as indicating stabilizing selection, while more change implies directional selection. The runs test in contrast, operates on the sequencing of steps, rather than on excursion. Applications of these tests to computer generated, simulated time series of known dynamical form and various levels of additive noise indicate that there is a fundamental asymmetry in the rate of type II errors of the tests based on excursion: they are all highly sensitive to noise in models of directional selection that result in a linear trend within a time series, but are largely noise immune in the case of a simple model of stabilizing selection. Additionally, the LRI method has a lower sensitivity than originally claimed, due to the large range of LRI rates produced by random walks. Examination of the published results of these tests show that they have seldom produced a conclusion that an observed evolutionary time series was due to directional selection, a result which needs closer examination in light of the asymmetric response of these tests.     

Limited capacity of working memory in unihemispheric random walks implies conceivable slow dispersal

Phenomenologically inspired by dolphins’ unihemispheric sleep, we introduce a minimal model for random walks with physiological memory. The physiological memory consists of long-term memory which includes unconscious implicit memory and conscious explicit memory, and working memory which serves as a multi-component system for integrating, manipulating and managing short-term storage. The model assumes that the sleeping state allows retrievals of episodic objects merely from the episodic buffer where these memory objects are invoked corresponding to the ambient objects and are thus object-oriented, together with intermittent but increasing use of implicit memory in which decisions are unconsciously picked up from historical time series. The process of memory decay and forgetting is constructed in the episodic buffer. The walker’s risk attitude, as a product of physiological heuristics according to the performance of objected-oriented decisions, is imposed on implicit memory. The analytical results of unihemispheric random walks with the mixture of object-oriented and time-oriented memory, as well as the long-time behavior which tends to the use of implicit memory, are provided, indicating the common sense that a conservative risk attitude is inclinable to slow movement.     

Sex‐biased dispersal,kin selection and the evolution of sexual conflict

There is growing interest in resolving the curious disconnect between the fields of kin selection and sexual selection. Rankin's (2011, J. Evol. Biol. 24 , 71–81) theoretical study of the impact of kin selection on the evolution of sexual conflict in viscous populations has been particularly valuable in stimulating empirical research in this area. An important goal of that study was to understand the impact of sex‐specific rates of dispersal upon the coevolution of male‐harm and female‐resistance behaviours. But the fitness functions derived in Rankin's study do not flow from his model's assumptions and, in particular, are not consistent with sex‐biased dispersal. Here, we develop new fitness functions that do logically flow from the model's assumptions, to determine the impact of sex‐specific patterns of dispersal on the evolution of sexual conflict. Although Rankin's study suggested that increasing male dispersal always promotes the evolution of male harm and that increasing female dispersal always inhibits the evolution of male harm, we find that the opposite can also be true, depending upon parameter values.     

The sex chromosome system can influence the evolution of sex‐biased dispersal

Sex‐biased dispersal is a much‐discussed feature in literature on dispersal. Diverse hypotheses have been proposed to explain the evolution of sex‐biased dispersal, a difference in dispersal rate or dispersal distance between males and females. An early hypothesis has indicated that it may rely on the difference in sex chromosomes between males and females. However, this proposal was quickly rejected without a real assessment. We propose a new perspective on this hypothesis by investigating the evolution of sex‐biased dispersal when dispersal genes are sex‐linked, that is when they are located on the sex chromosomes. We show that individuals of the heterogametic sex disperse relatively more than do individuals of the homogametic sex when dispersal genes are sex‐linked rather than autosomal. Although such a sex‐biased dispersal towards the heterogametic sex is always observed in monogamous species, the mating system and the location of dispersal genes interact to modulate sex‐biased dispersal in monandry and polyandry. In the context of the multicausality of dispersal, we suggest that sex‐linked dispersal genes can influence the evolution of sex‐biased dispersal.     

Mating timing,dispersal and local adaptation in patchy environments

Dispersal is a life‐history trait that can evolve under various known selective pressures as identified by a multitude of theoretical and empirical studies. Yet only few of them are considering the succession of mating and dispersal. The sequence of these events influences gene flow and consequently affects the dynamics and evolution of populations. We use individual‐based simulations to investigate the evolution of the timing of dispersal and mating, i.e. mating before or after dispersal. We assume a discrete insect metapopulation in a heterogeneous environment, where populations may adapt to local conditions and only females are allowed to disperse. We run the model assuming different levels of species habitat tolerance, carrying capacity, and temporal environmental variability. Our results show that in species with narrow habitat tolerance, low to moderate dispersal evolves in combination with mating after dispersal (post‐dispersal mating). With such a strategy dispersing females benefit from mating with a resident male, as their offspring will be better adapted to the local habitat conditions. On the contrary, in species with wide habitat tolerance higher dispersal rates in combination with pre‐dispersal mating evolves. In this case individuals are adapted to the ‘average’ habitat where pre‐dispersal mating conveys the benefit of carrying relatives’ genes into a new population. With high dispersal rates and large population size, local adaptation and kin structure both vanish and the temporal sequence of dispersal and mating may become a (nearly) neutral trait.     

Linked selection,demography and the evolution of correlated genomic landscapes in birds and beyond

Selection has a deep impact on the distribution of genetic diversity and population differentiation along the genome (the genomic landscapes of diversity and differentiation), reducing diversity and elevating differentiation not only at the sites it targets, but also at linked neutral sites. Fuelled by the high‐throughput sequencing revolution, these genomic footprints of selection have been extensively exploited over the past decade with the aim to identify genomic regions involved in adaptation and speciation. However, while this research has shown that the genomic landscapes of diversity and differentiation are usually highly heterogeneous, it has also led to the increasing realization that this heterogeneity may evolve under processes other than adaptation or speciation. In particular, instead of being an effect of selective sweeps or barriers to gene flow, accentuated differentiation can evolve by any process reducing genetic diversity locally within the genome (Charlesworth, 1998 ), including purifying selection at linked sites (background selection). In particular, in genomic regions where recombination is infrequent, accentuated differentiation can evolve as a by‐product of diversity reductions unrelated to adaptation or speciation (Cruickshank & Hahn, 2014 ; Nachman & Payseur, 2012 ; Noor & Bennett, 2009 ). In such genomic regions, linkage extends over physically larger genome stretches, and selection affects a particularly high number of linked neutral sites. Even though the effects of selection on linked neutral diversity (linked selection) within populations are well documented (Cutter & Payseur, 2013 ), recent observations of diversity and differentiation landscapes that are highly correlated even among independent lineages suggest that the effects of long‐term linked selection may have a deeper impact on the evolution of the genomic landscapes of diversity and differentiation than previously anticipated. The study on Saxicola stonechats by Van Doren et al. ( 2017 ) reported in the current issue of Molecular Ecology lines in with a rapidly expanding body of evidence in this direction. Correlations of genomic landscapes extending from within stonechats to comparisons with Ficedula flycatchers add to recent insights into the timescales across which the effects of linked selection persist. Absent and inverted correlations of genomic landscapes in comparisons involving an island taxon, on the other hand, provide important empirical clues about the role of demographic constraints in the evolution of the genomic landscapes of diversity and differentiation.     

How landscapes affect the evolution of dispersal behaviour in reef fishes: results from an individual‐based model

The vast majority of tropical reef fishes have a sedentary adult phase and pelagic larval phase that is potentially highly dispersive. Dispersal may be favoured by a wide range of factors including the arrangement of suitable habitat in space. In this paper the dispersal strategy of individuals is followed and allowed to evolve in a simplified model of three different landscapes: an enclosed sea, an open archipelago and a barrier reef. The three landscapes have very different characteristics, but all have similar spatial clumping of reef habitat. In all landscapes, as minimum time to settlement increases, evolved movement strategy also increases and longer settlement windows favour dispersal. In the archipelago movement is not maximized until the minimum pelagic duration is longer than in the other landscapes. The model predicts that, given the same pelagic duration, species from enclosed seas should have more dispersive behaviours than those from open archipelagos, because of the density of habitat and the aggregation of habitat in space affect the likelihood of larvae finding suitable habitat for settlement.     

Estimating species' absence, colonization and local extinction in patchy landscapes: an application of occupancy models with rodents

Making an inference on the absence of a species in a site is often problematic, due to detection probability being, in most cases, <1. Inference is more complicated if detection probability, together with distribution patterns, vary during the year, since the possibility of inferring a species absence, at reasonable costs, may be possible only in certain periods. Our aim here is to show how such challenging situations can be by tackled by applying some recently developed occupancy models combined with sample size (number of repeated surveys) estimation. We thus analysed the distribution of two rodents Myodes glareolus and Mus musculus domesticus in a fragmented landscape in central Italy pointing out how it is possible to identify true absences, non-detections, extinctions/colonizations and determine seasonal values of detection probability.     

The arrangement of resources in patchy landscapes: effects on distribution, survival, and resource acquisition of chironomids

The spatial arrangement of resources in patchy habitats influences the distribution of individuals and their ability to acquire resources. We used Chironomus riparius, a ubiquitous aquatic insect that uses leaf particles as an important resource, to ask how the dispersion of resource patches influences the distribution and resource acquisition of mobile individuals in patchy landscapes. Two experiments were conducted in replicated laboratory landscapes (38×38 cm) created by arranging sand and leaf patches in a 5×5 grid so that the leaf patches were either aggregated or uniformly dispersed in the grid. One-day-old C. riparius larvae were introduced into the landscapes in one of three densities (low, medium, high). In experiment 1, we sampled larvae and pupae by coring each patch in each landscape 3, 6, 12, or 24 days after adding larvae. In experiment 2, emerging adults were collected daily for 42 days from each patch in each landscape. In aggregated landscapes, individuals were aggregated in one patch type or the other during a particular developmental stage, but the ”preferred” type changed depending on developmental stage and initial density. Adult emergence was lower by about 30% in all aggregated landscapes. In dispersed landscapes, individuals used both types of patch throughout their life cycles at all initial densities. Thus, patch arrangement influences the distribution of mobile individuals in landscapes, and it influences resource acquisition even when average resource abundance is identical among landscapes. Regardless of patch arrangement, high initial density caused accumulation of early instars in edge patches, 75% mortality of early instars, a 25% increase in development time, and a 60% reduction in adult emergence. Because mortality was extremely high among early-instar larvae in high-density treatments, we do not have direct evidence that the mechanism by which patch arrangement operates is density dependent. However, the results of our experiments strongly suggest that dispersion of resource patches across a landscape reduces local densities by making non-resource patches available for use, thereby reducing intraspecific competition. Received: 20 July 1999 / Accepted: 28 January 2000     

Adaptive walks on behavioural landscapes and the evolution of optimal behaviour by natural selection

Summary One of the main challenges to the adaptationist programme in general and to the use of optimality models in behavioural and evolutionary ecology in particular is that natural selection need not optimise fitness. This challenge is addressed by considering the evolution of optimal patch choice by natural selection. The behavioural model is based on a state variable approach in which a strategy consists of a sequence denoting the patch to be visited as a function of the organism's state and time. The optimal strategy maximises expected terminal reproduction. The fitnesses of alternative strategies are computed by iteration of the associated equations for fitness; this characterises the adaptive behavioural landscape. There may be enormous numbers of strategies that have near optimal fitnesses. A population model is used to connect frequencies of behavioural types from one generation to the next. Theories on adaptive walks on fitness landscapes are considered in the context of behaviour. The main result is that within the context of optimality arguments at selective equilibrium, sub-optimal behaviours can persist. General implications for research in behavioural ecology, including tests of behavioural theories, are discussed.     

Edge effects in patchy seagrass landscapes: The role of predation in determining fish distribution

Predation is often described as an underlying mechanism to explain edge effects. We assessed the importance of predation in determining edge effects in seagrass using two approaches: a video survey to sample predators at small scales across seagrass edges, and a tethering experiment to determine if predation was an underlying mechanism causing edge effects. Underwater videos were placed at four positions: middle of seagrass patches; edge of seagrass; sand immediately adjacent to seagrass and sand distant from seagrass. Fish abundances and the time fish spent in view were measured. The main predatory fish (Australian salmon, Arripis spp.) spent more time over adjacent sand than other positions, while potential prey species (King George whiting, Sillaginodes punctata (Cuvier), recruits) were more common in the middle of seagrass patches. Other species, including the smooth toadfish, Tetractenos glaber (Freminville), and King George whiting adults, spent more time over sand adjacent to seagrass than distant sand, which may be related to feeding opportunities. King George whiting recruits and pipefish (Stigmatopora spp.) were tethered at each of the four positions. More whiting recruits were preyed upon at outer than inner seagrass patches, and survival time was greater in the middle of shallow seagrass patches than other positions. Relatively few pipefish were preyed upon, but of those that were, survival time was lower over sand adjacent to seagrass than at the seagrass edge or middle. Video footage revealed that salmon were the dominant predators of both tethered King George whiting recruits and pipefish. The distribution of predators and associated rate of predation can explain edge effects for some species (King George whiting) but other mechanisms, or combinations of mechanisms, are determining edge effects for other species (pipefish).     

The evolution of dispersal

A non-local model for dispersal with continuous time and space is carefully justified and discussed. The necessary mathematical background is developed and we point out some interesting and challenging problems. While the basic model is not new, a spread parameter (effectively the width of the dispersal kernel) has been introduced along with a conventional rate paramter, and we compare their competitive advantages and disadvantages in a spatially heterogeneous environment. We show that, as in the case of reaction-diffusion models, for fixed spread slower rates of diffusion are always optimal. However, fixing the dispersal rate and varying the spread while assuming a constant cost of dispersal leads to more complicated results. For example, in a fairly general setting given two phenotypes with different, but small spread, the smaller spread is selected while in the case of large spread the larger spread is selected. S. Martinez was partially supported by Fondecyt 1020126 and Fondecyt Lineas Complementarias 8000010. K. Mischaikow was supported in part by NSF Grant DMS 0107396. Key words or phases:Non-local dispersal – Integral kernel – Evolution of dispersal     

Woodland birds in patchy landscapes: the evidence base for strategic networks

Habitat creation and management within wooded networks is a potentially effective strategy to reduce ecological isolation and the deleterious effects of fragmentation. However, questions remain over the relative advantages of different approaches, e.g. buffering patches vs. increasing connectivity. Potential effects of woodland fragmentation include reduction in regional woodland cover, reduced patch size, edge effects with loss of core habitat, and increased isolation with disruption of dispersal and metapopulation dynamics. We adopt an evidence-based approach to review how each of these affects woodland birds with an emphasis on studies from the UK and use this to identify management priorities for mitigation. There is evidence for both patch area and composition effects: larger woodlands support more woodland bird species, and woods located within sparsely wooded landscapes are less valuable to specialist woodland species. Bird assemblages show a nested pattern with respect to area, and thus species found in small woods also occur in large woods but not vice versa. However, small woods may be preferred by a few edge species, while small woods also have greater variability in bird species composition. Consideration of the metapopulation dynamics of specialist species with poor dispersal shows that creating or buffering large woodlands is more efficient than a greater total area of small fragments. Connectivity appears most useful for widespread generalist species with almost continuous populations. Woodland structure and quality are of overwhelming importance: as well as mature woodland, young growth, scrub and edges are also key components. There is an urgent need to examine the relationship between nest predation and landscape structure within UK woodlands.     

Investigating the dispersal routes used by an invasive amphibian, Lithobates catesbeianus, in human-dominated landscapes

Clarifying how species move across and utilize human-modified landscapes is key to the conservation of declining populations, as well as to the management and control of invasive species. The North American bullfrog (Lithobates catesbeianus) is a globally distributed invasive amphibian that has been implicated in the decline of native amphibians across its invasive range and may also act as a transport vector for a number of deadly amphibian pathogens. Identifying the landscape-level features that facilitate or hinder this species as it moves across an ever-changing landscape is necessary to inform control efforts and limit this species’ impact on already declining amphibian populations. We conducted surveys of 243 wetlands across the Colorado Front Range and used an information-theoretic approach to evaluate the contribution of wetland-specific characteristics and landscape-level factors in determining the detection of bullfrog populations and breeding bullfrog populations. Specifically, our goal was to determine whether features related to overland dispersal or to the connectivity of wetlands were better predictors of bullfrog occurrence. Our results indicated that landscape-level factors that may either hinder or facilitate overland movement, such as topographic complexity and the density of wetlands, were the best predictors of bullfrog occurrence at the scale of our analysis, rather than characteristics relating to the connectivity of wetlands to lotic waterway systems. We suggest that when considering the control or eradication of this species, efforts should be directed at reducing hydroperiod of wetlands and should target regions with a high density of wetlands and/or low topographic relief.